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Life_Insurance_and_Annuities (part 1) stdt

Insurance pricing ignore expenses and risk load focus

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Unformatted text preview: 02 Assume Assume Premiums paid at beginning of year Claims paid at end of year What does this tell us? Pricing 1-Year Term Find fair premium for $100,000 1-year term for 40 year-old (Interest rate = 10% Insurer’s cash flows: Pricing 1-Year Term Find fair premium for $100,000 1-year term Find for 41 year old (Interest rate = 10%) 41 year Insurer’s cash flows: Insurer’s Pricing 1-Year term Premium increases as probability of dying Premium increases increases Pricing 2-Year Term Find fair premium for $100,000 2-year term Find for 40 year-old for Insurer’s claim costs Beg. Of Year 1 End of Year 1 -$100,000 with prob. 0.00302 End of Year 2 -$100,000 with prob. X -$100,000 $0 with prob. 0.99698 $0 with prob. 1-X Pricing 2-Year Term What is X, the probability of a 40 year-old dying in his What the 42nd year? 42 Mortality table: Age Number of People Number of Deaths 40 937723 2832 41 934891 3076 Probability of 40 year-old dying in 41st year = Probability of 40 year-old dying in 42nd year = Probability Pricing 2-Year Term (Single premium) Insurer’s expected cash flows: Beg. Of Year End of Year 1 Expected claim costs Premium = PV of expected claim costs = End of Year 2 Pricing 2-Year Term (Level Premium) Same premium paid at beginning of each Same year (if insured survives) year Insurer’s expected cash flows Beg. Of Year 1 End of Year 1 Premium Premium x 0.99698 -$302 End of Year 2 -$328 Find Premium so that PV of expected premiums = PV of expected claims Pricing 2-year Term Premium + (p x Premium)/(1+i) Premium = PV of E(Cash inflows) PV Where p = probability of receiving the 2nd premium premium A Comparison Expected costs of three alternative methods Expected of obtaining coverage: of Beginning Beginning of 1st Year of nd Beginning of 2nd Year Present Successive one year policies $275 $299 x 0.99698 = $298 $546 Level premium two-year term Level policy policy $286 $286 x 0.99698 = $285 $546 Single premium two-year term Single policy policy $546 $0 $546 Implications Annual premiums for successive term policies reflect Annual the annual cost of insuring the Annual cost = $275 and $298 Wi...
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